%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:52:25 AM UTC 2026
% Result : Unsatisfiable 3.79s 2.40s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 208 ( 28 ~; 28 |; 0 &; 152 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(basis_decl,type,
basis: $i > $i > $o ).
thf(cx_decl,type,
cx: $i ).
thf(f_decl,type,
f: $i ).
thf(subset_sets_decl,type,
subset_sets: $i > $i > $o ).
thf(union_of_members_decl,type,
union_of_members: $i > $i ).
thf(top_of_basis_decl,type,
top_of_basis: $i > $i ).
thf(element_of_set_decl,type,
element_of_set: $i > $i > $o ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(element_of_collection_decl,type,
element_of_collection: $i > $i > $o ).
thf(equal_sets_decl,type,
equal_sets: $i > $i > $o ).
thf(f10_decl,type,
f10: $i > $i > $i > $i ).
thf(in_1st_set_decl,type,
in_1st_set: $i > $i > $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ f10 ) ) @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_37) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ f10 ) ) @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
f @ ( cx @ basis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1a_1) ).
thf(14,plain,
f @ ( cx @ basis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ subset_sets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_1) ).
thf(29,plain,
! [A: $i] : ( A @ ( A @ subset_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ element_of_set ) )
| ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_3) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ element_of_collection ) )
| ~ ( C @ ( A @ element_of_set ) )
| ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ f10 ) ) @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_38) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( B @ f10 ) ) @ element_of_collection ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ top_of_basis @ ( A @ element_of_collection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ basis ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_28) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ union_of_members @ equal_sets ) )
| ~ ( B @ ( A @ basis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
~ ( cx @ ( f @ top_of_basis @ union_of_members @ subset_sets ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1a_2) ).
thf(15,plain,
~ ( cx @ ( f @ top_of_basis @ union_of_members @ subset_sets ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ f1 ) @ ( A @ element_of_set ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_1) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ f1 ) @ ( A @ element_of_set ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_3) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset_sets ) )
| ~ ( B @ ( A @ equal_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ in_1st_set ) @ element_of_set ) )
| ( B @ ( A @ subset_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_4) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ in_1st_set ) @ element_of_set ) )
| ( B @ ( A @ subset_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ in_1st_set ) @ element_of_set ) )
| ( B @ ( A @ subset_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_5) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ in_1st_set ) @ element_of_set ) )
| ( B @ ( A @ subset_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ subset_sets ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ element_of_set ) )
| ~ ( A @ ( C @ element_of_set ) )
| ~ ( B @ ( A @ subset_sets ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ f1 ) @ element_of_collection ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ f1 ) @ element_of_collection ) )
| ~ ( B @ union_of_members @ ( A @ element_of_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[25,14,29,21,27,23,15,17,32,34,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n019.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 20:29:50 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.19 % [INFO] Parsing done (186ms).
% 1.41/1.20 % [INFO] Running in sequential loop mode.
% 2.00/1.61 % [INFO] eprover registered as external prover.
% 2.00/1.62 % [INFO] Scanning for conjecture ...
% 2.18/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.18/1.75 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.18/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.18/1.77 % [INFO] Type checking passed.
% 2.18/1.78 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.79/2.40 % External prover 'e' found a proof!
% 3.79/2.40 % [INFO] Killing All external provers ...
% 3.79/2.40 % Time passed: 1843ms (effective reasoning time: 1195ms)
% 3.79/2.40 % Axioms used in derivation (11): basis_for_topology_28, set_theory_1, union_of_members_3, set_theory_4, union_of_members_2, set_theory_3, topology_generated_38, union_of_members_1, set_theory_2, set_theory_5, topology_generated_37
% 3.79/2.40 % No. of inferences in proof: 27
% 3.79/2.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1843 ms resp. 1195 ms w/o parsing
% 3.79/2.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.79/2.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------